arXiv subjects

Jiahua Tian

Publications and source records attributed to Jiahua Tian.

At least 19 recordsLinked to original sources

arXiv2026

Pseudo-Gauge Stabilizers and Fibration Structure of the Cooper--Frye Map at Freeze-Out

We study the pseudo-gauge transformation (PGT) freedom at freeze-out in relativistic spin hydrodynamics. The Cooper--Frye map is shown to factor through the quotient of freeze-out data by a universal stabilizer, yielding a stratified fibration over the space of thermodynamic Lagrange multipliers. This classifies observables into base and fiber types, bounds the number of independent PGT-sensitive observables by the family-restricted fiber dimension, and implies cross-observable consistency relations. Applied to heavy-ion polarization data, the fibration structure provides a structural interpretation of the tension between $Λ$ polarization and $ϕ$-meson spin alignment as evidence that the vorticity-dominated response sector may need to be enlarged with local field-correlation data. We show that Weyl-anomaly-induced currents studied recently are classified as base observables and recover the known Belinfante--canonical obstruction $Ω_{ab}\neq\varpi_{ab}$ from the stabilizer condition.

hep-th↗

arXiv2026

Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries

We present a quantum mechanical approach to understanding the Hilbert space and the defect Hilbert spaces associated with line operators of BF theory combined with level-$k$ Chern-Simons theory. The defect Hilbert spaces are closely related to the category of $*$-representations of the $C^*$-algebra of the compactly supported sections of the Fell line bundle over the conjugation action groupoid $G//_{\mathrm Ad} G$, and the structure of this category and the groupoid action on the objects of this category is interpreted quantum mechanically. We show that the action of the line operators on the Hilbert space of the $BF+kCS$ TQFT is given concretely by a convolution between the kernels that represent the line operators, and that the codimension-$2$ twist and the codimension-$1$ prequantum line bundle arise as two transgressions of the same universal level $k\in H^4(BG,\mathbb{Z})$. For finite gauge group, the resulting convolution-eigenvalue formula is identified with the Verlinde formula for the (twisted) Drinfeld double $D^ω(G)$ via an explicit phase-by-phase match with the known finite modular data. For compact Lie group, the convolution-kernel eigenvalues coincide in the regular sector with the semiclassical Hopf-link $S$-kernel, identifying two complementary derivations of the same modular data.

hep-th↗

arXiv2026

Candidate Gaugings of Categorical Continuous Symmetry

Different gaugings of the global symmetry of a quantum field theory are closely related to its various phases. In this work, we study candidate gaugeable symmetries by analyzing candidate Lagrangian algebra data in the Drinfeld center of a symmetry category $\mathscr{C}^k(G)$ associated to a QFT with continuous global $G$-symmetry and possible 't Hooft anomaly labeled by an integer $k$. We use the combination of the $BF$ theory and the level-$k$ Chern-Simons theory with gauge group $G$ as a semiclassical kernel-theoretic model for the corresponding SymTFT. Under two explicit assumptions, namely that this $BF{+}k$CS theory provides the relevant SymTFT model and that the common $+1$ eigenspaces of the resulting modular kernels detect candidate Lagrangian algebra data in the continuous setting, we derive candidate modular $S$- and $T$-kernels from Hopf-link and framing correlators in $S^3$ semi-classically. We then use these kernels to obtain candidate modular invariants and candidate gaugings. The resulting formulas recover the established cases and suggest a possible extension of this kernel-theoretic picture to compact Lie groups.

hep-th↗

arXiv2026

Categorical Symmetries via Operator Algebras

We propose that the symmetry category associated to a 2D quantum field theory with 0-form $G$-symmetry with 't Hooft anomaly $k\in H^4(BG,\mathbb{Z})$ for a large class of Lie groups $G$ is the category of twisted measurable fields of Hilbert spaces over $G$ denoted by $\mathrm{Hilb}^k(G)$, which is equivalent to the category of unitary representations of $C_0(G)$ with convolution product twisted by a multiplicative bundle gerbe labeled by $k$ denoted by $\textbf{Rep}^k(C_0(G))$. We find that the Drinfeld center of the symmetry category $\mathcal{Z}(\mathrm{Hilb}^{k}(G))$ equivalent to the category of unitary representations of the groupoid $C^*$-algebra of the Fell line bundle $Σ_k$ over the conjugation action groupoid $G//_{\rm Ad} G$, denoted by $\textbf{Rep}(C^*(G//_{\rm Ad}G,Σ_k))$, where the twist is characterized by the transgression $τ(k)\in H^2(G//_{\rm Ad}G,U(1))$. To the full generality, our framework applies to a Lie group $G$ that is a direct product of a compact connected Lie group and a number of $\mathbb{R}$ or $GL(1,\mathbb{C})$ factors. We compute the braiding of anyon lines in the bulk 3D SymTFT from this formalism. Finally we provide physical examples for abelian and non-abelian $G$, and discuss the physical consequences of flat gauging continuous global symmetries.

hep-th↗

arXiv2025

Anomaly of Continuous Symmetries from Topological Defect Network

We show that the 't Hooft anomaly of a quantum field theory with continuous flavor symmetry can be detected from rearrangements of the topological defect webs implementing the global symmetry in general spacetime dimension, which is concretized in 2D by the F-moves of the defect lines. Via dualizing the defects to flat background gauge field configurations, we characterize the 't Hooft anomaly by various cohomological data of the symmetry group, where the cohomology of Lie groups with discrete topology plays the central role. We find that an extra dimension emerges naturally as a consequence of the mathematical description of the 't Hooft anomaly in the case of flat gauging.

hep-th↗

arXiv2025

Conformal Fields from Neural Networks

We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be computed using the parameter space description of the neural network. Exact four-point correlators are computed in a number of examples, and we perform a 4D conformal block decomposition that elucidates the spectrum. In some examples the analysis is facilitated by recent approaches to Feynman integrals. Generalized free CFTs are constructed using the infinite-width Gaussian process limit of the neural network, enabling a realization of the free boson. The extension to deep networks constructs conformal fields at each subsequent layer, with recursion relations relating their conformal dimensions and four-point functions. Numerical approaches are discussed.

hep-th↗

arXiv2025

Categorical Continuous Symmetry

We define the symmetry category in 1+1d for continuous 0-form $G$-symmetry to be $\textbf{Sky}^τ(G)$, the category of skyscraper sheaves of finite dimensional vector spaces with finite support on the group manifold of $G$, where $τ\in H^4(BG,\mathbb{Z})$ is the anomaly. We propose that the corresponding 2+1d SymTFT is described by the Drinfeld center of $\textbf{Sky}^τ(G)$. We show explicitly the way that $τ$ twists the convolution tensor product of the objects of $\textbf{Sky}^τ(G)$. As a concrete example, we present the $S$ and $T$-matrices for the simple anyons of the resulting $Z(\textbf{Sky}^τ(G))$ category for $G = U(1)$, both for the cases without or with anomaly and discuss the topological boundary conditions as Lagrangian algebra of $Z(\textbf{Sky}^τ(U(1)))$. We also present the definition of $\textbf{Sky}^τ(G)$ and $Z(\textbf{Sky}^τ(G))$ for the non-abelian case of $G=SU(2)$, as well as the speculated modular data. We point out that in order to have a physically relevant center and Lagrangian algebras it is necessary to generalize $\textbf{Sky}^τ(G)$ to a larger category, which we argue to be closely related to the category of quasi-coherent sheaves on $G_\mathbb{C}$ with convolution tensor product twisted by $τ$.

hep-th↗

arXiv2025

Symmetry, Symmetry Topological Field Theory and von Neumann Algebra

We study the additivity and Haag duality of the von Neumann algebra of a quantum field theory $\mathcal{T}_\mathcal{F}$ with 0-form (and the dual $(d-2)$-form) (non)-invertible global symmetry $\mathcal{F}$. We analyze the symmetric (uncharged) sector von Neumann algebra of $\mathcal{T}_\mathcal{F}$ with the inclusion of bi-local and bi-twist operators in it. We establish the connection between the existence of these non-local operators in $\mathcal{T}_\mathcal{F}$ and certain properties of the Lagrangian algebra $\mathcal{L}$ of the extended operators in the corresponding symmetry topological field theory (SymTFT). We prove that additivity or Haag duality of the symmetric sector von Neumann algebra is violated when $\mathcal{L}$ satisfies specific criteria, thus generalizing the result of Shao, Sorce and Srivastava to arbitrary dimensions. We further demonstrate the SymTFT construction via concrete examples in two dimensions.

hep-th↗

arXiv2025

Higher Form and Higher Group Symmetries via Mirror Symmetry

In this work we uncover a connection that relates the 1-form and the 2-group symmetries of 5D SCFTs derived from geometric engineering methods to monodromies of the corresponding B-models via mirror symmetry. Viewing defects as branes wrapping relative cycles in a non-compact CY3, we find that the defect groups can be read off from the VEVs of the corresponding line operators at the leading order. Via mirror map, we find that both the 1-form and the 2-group symmetries of the SCFT are related to the monodromy at the large radius point in the B-model. Additionally, we recursively obtain closed-form expressions of instanton expansions of the VEV of Wilson lines of certain 5D theories among which some have not been obtained so far using localization methods. We further conjecture that the 2-group symmetry is given by the Mordell-Weil torsion of the universal special geometry associated to the theory, generalizing the conjecture for rank-1 theories.

hep-th↗

arXiv2025

Symmetry Topological Field Theory for Flavor Symmetry

In this Letter, we demonstrate that the Symmetry Topological Field Theory (SymTFT) associated to a Quantum Field Theory (QFT) with continuous non-abelian $G$-flavor symmetry is a $BF$-theory with gauge group $G$. We show that gauging $G$-symmetry with a flat connection yields a theory with global symmetry characterized by exchanging the conjugate variables in the quantization of $BF$-theory. We construct the extended operators that generate the $G$-flavor symmetry and the $(d-2)$-form $\text{Rep}(G)$-symmetry of the gauged QFT. We demonstrate that $BF$-theory arises as the theory characterizing $G$-flavor symmetry of a QFT in the AdS/CFT setup. 't Hooft anomalies of the $G$-flavor symmetry are realized as extra terms in the action.

hep-th↗

arXiv2025

A Tale of Bulk and Branes: Symmetry TFT of 6D SCFTs from IIB/F-theory

We study the 7D Symmetry Topological Field Theory (SymTFT) associated to a 6D SCFT from the IIB/F-theory geometric engineering approach. The 6D (2,0) or (1,0) SCFT is constructed from IIB on a non-compact complex surface possibly with 7-branes. We derive the general form of 7D SymTFT actions from the compactification of IIB action on the boundary link of the base manifold of an elliptic Calabi-Yau threefold, for both the cases with or without flavor 7-branes intersecting the boundary link. Along the way we found new terms in the SymTFT action from the worldvolume action of flavor 7-branes involving the flavor center symmetries. We crosscheck the results against those obtained from either holographic constructions or the dual M-theory picture. Our construction potentially leads to a classification of the 7D SymTFTs which parallels the known geometric classification of the 6D SCFTs.

hep-th↗

arXiv2024

3d $N=2$ theories from M-theory on CY4 and IIB brane box

We study 3D $N=2$ supersymmetric field theories geometrically engineered from M-theory on non-compact Calabi-Yau fourfolds (CY4). We establish a detailed dictionary between the geometry and topology of non-compact CY4 and the physics of 3D $N=2$ theories in three different regimes. The first one is the Coulomb branch description when the CY4 is smooth. The second one is non-abelian gauge theory when the CY4 has a degenerate $\mathbb{P}^1$-fibration structure. The third one is the strongly coupled SCFT from a CY4 singularity. We find interesting flavor symmetry enhancements in the singular limit of CY4, as well as an interesting and previously unexplored phenomenon in 3D, termed ``flavor symmetry duality''. Many examples are analyzed with an emphasis on toric CY4s and $\mathbb{C}^4$ orbifolds with crepant resolutions. We develop a new brane box method to study the physics of Coulomb branch of 3D $N=2$ theory that admits a toric construction. Via IIB/M-theory duality we find that the brane box diagram living in $\mathbb{R}^3$ can be physically realized as a configuration of intersecting 4-branes which are extended objects in 8D maximal supersymmetric theory, which is shown to be consistent via various chains of dualities. The rank, effective gauge coupling and certain hints to flavor symmetry enhancement of the 3D $N=2$ theory are read off from the brane box and cross-checked against the results obtained from geometric engineering. The exotic branes in 8D maximal supersymmetric theory and the 4-string junctions thereof are shown to play a crucial role in the construction of the brane box.

hep-th↗

arXiv2023

Electric-Magnetic Duality in a Class of $G_2$-Compactifications of M-theory

We study electric-magnetic duality in compactifications of M-theory on twisted connected sum (TCS) $G_2$ manifolds via duality with F-theory. Specifically, we study the physics of the D3-branes in F-theory compactified on a Calabi-Yau fourfold $Y$, dual to a compactification of M-theory on a TCS $G_2$ manifold $X$. $\mathcal{N}=2$ supersymmetry is restored in an appropriate geometric limit. In that limit, we demonstrate that the dual of D3-branes probing seven-branes corresponds to the shrinking of certain surfaces and curves, yielding light particles that may carry both electric and magnetic charges. We provide evidence that the Minahan-Nemeschansky theories with $E_n$ flavor symmetry may be realized in this way. The $SL(2,\mathbb{Z})$ monodromy of the 3/7-brane system is dual to a Fourier-Mukai transform of the dual IIA/M-theory geometry in this limit, and we extrapolate this monodromy action to the global compactification. Away from the limit, the theory is broken to $\mathcal{N}=1$ supersymmetry by a D-term.

hep-th↗

arXiv2022

$6$D Anomaly-Free Matter Spectrum in F-theory on Singular Spaces

In this paper we study the 6d localized charged matter spectrum of F-theory directly on a singular elliptic Calabi-Yau 3-fold, i.e. without smoothing via resolution or deformation of the entire fibration. Given only the base surface, discriminant locus, and the $SL(2,\mathbb{Z})$ local system, we propose a general prescription for determining the charged matter spectrum localized at intersections of seven-branes, using the technology of string junctions. More precisely, at each codimension-$2$ collision of seven-branes, we determine the local seven-brane content and compute the number of massless string junctions modulo the action of the $SL(2,\mathbb{Z})$ monodromy. We find agreement with the predicted results from $6$d anomaly cancellation in all cases considered. Examples include a generic Weierstrass model with arbitrary Kodaira fiber intersecting an $I_1$, as well as cases with jointly charged matter localized at intersections of non-abelian seven-branes.

hep-th↗

arXiv2022

5D and 6D SCFTs from $\mathbb{C}^3$ orbifolds

We study the orbifold singularities $X=\mathbb{C}^3/Γ$ where $Γ$ is a finite subgroup of $SU(3)$. M-theory on this orbifold singularity gives rise to a 5d SCFT, which is investigated with two methods. The first approach is via 3d McKay correspondence which relates the group theoretic data of $Γ$ to the physical properties of the 5d SCFT. In particular, the 1-form symmetry of the 5d SCFT is read off from the McKay quiver of $Γ$ in an elegant way. The second method is to explicitly resolve the singularity $X$ and study the Coulomb branch information of the 5d SCFT, which is applied to toric, non-toric hypersurface and complete intersection cases. Many new theories are constructed, either with or without an IR quiver gauge theory description. We find that many resolved Calabi-Yau threefolds, $\widetilde{X}$, contain compact exceptional divisors that are singular by themselves. Moreover, for certain cases of $Γ$, the orbifold singularity $\mathbb{C}^3/Γ$ can be embedded in an elliptic model and gives rise to a 6d (1,0) SCFT in the F-theory construction. Such 6d theory is naturally related to the 5d SCFT defined on the same singularity. We find examples of rank-1 6d SCFTs without a gauge group, which are potentially different from the rank-1 E-string theory.

hep-th↗

arXiv2022

Gauging Discrete Symmetries of $T_N$-theories in Five Dimensions

We study the gauging of a discrete $\mathbb{Z}_3$ symmetry in the five-dimensional superconformal $T_N$ theories. We argue that this leads to an infinite sequence of five-dimensional superconformal theories with either $E_6 \times SU(N)$ or $SU(3)\times SU(N)$ global symmetry group. In the $M$-theory realisation of $T_N$ theories as residing at the origin in the Calabi-Yau orbifolds ${\mathbb{C}^3 \over {\mathbb{Z}_N \times \mathbb{Z}_N}}$ we identify the $\mathbb{Z}_3$ symmetry geometrically and the new theories arise from $M$-theory on the non-Abelian orbifolds $({\mathbb{C}^3 \over {\mathbb{Z}_N \times \mathbb{Z}_N}})/{\mathbb{Z}_3}$. On the other hand, in the $(p,q)$ 5-brane web description in Type IIB theory, the symmetry combines the $U$-duality symmetry with a rotation in space, defining a so-called $U$-fold background, where the $E_6$ symmetry is manifest.

hep-th↗

arXiv2021

Elliptic Calabi-Yau fivefolds and 2d (0,2) F-theory landscape

In this paper, we initiate the study of the 2d F-theory landscape based on compact elliptic Calabi-Yau fivefolds. In particular, we determine the boundary models of the landscape using Calabi-Yau fivefolds with the largest known Hodge numbers $h^{1,1}$ and $h^{4,1}$. The former gives rise to the largest geometric gauge group in the currently known 2d (0,2) supergravity landscape, which is $E_8^{482\,632\,421}\times F_4^{3\,224\,195\,728}\times G_2^{11\,927\,989\,964}\times SU(2)^{25\,625\,222\,180}$. Besides that, we systematically study the hypersurfaces in weighted projective spaces with small degrees, and check the gravitational anomaly cancellation. Moreover, we also initiate the study of singular bases in 2d F-theory. We find that orbifold singularities on the base fourfold have non-zero contributions to the gravitational anomaly.

hep-th↗

arXiv2019

Kahler Moduli Stabilization and the Propagation of Decidability

Diophantine equations are in general undecidable, yet appear readily in string theory. We demonstrate that numerous classes of Diophantine equations arising in string theory are decidable and propose that decidability may propagate through networks of string vacua due to additional structure in the theory. Diophantine equations arising in index computations relevant for D3-instanton corrections to the superpotential exhibit propagation of decidability, with new and existing solutions propagating through networks of geometries related by topological transitions. In the geometries we consider, most divisor classes appear in at least one solution, significantly improving prospects for Kahler moduli stabilization across large ensembles of string compactifications.

hep-th↗